% \chapter{外文资料原文}
% \label{cha:engorg}
% As one of the most widely used techniques in operations research, {\em
%   mathematical programming} is defined as a means of maximizing a quantity known
% as {\em objective function}, subject to a set of constraints represented by
% equations and inequalities. Some known subtopics of mathematical programming are
% linear programming, nonlinear programming, multiobjective programming, goal
% programming, dynamic programming, and multilevel programming$^{[1]}$.

% It is impossible to cover in a single chapter every concept of mathematical
% programming. This chapter introduces only the basic concepts and techniques of
% mathematical programming such that readers gain an understanding of them
% throughout the book$^{[2,3]}$.


% \section{Single-Objective Programming}
% The general form of single-objective programming (SOP) is written
% as follows,
% \begin{equation}\tag*{(123)} % 如果附录中的公式不想让它出现在公式索引中，那就请
%                              % 用 \tag*{xxxx}
% \left\{\begin{array}{l}
% \max \,\,f(x)\\[0.1 cm]
% \mbox{subject to:} \\ [0.1 cm]
% \qquad g_j(x)\le 0,\quad j=1,2,\cdots,p
% \end{array}\right.
% \end{equation}
% which maximizes a real-valued function $f$ of
% $x=(x_1,x_2,\cdots,x_n)$ subject to a set of constraints.

% \newtheorem{mpdef}{Definition}[chapter]
% \begin{mpdef}
% In SOP, we call $x$ a decision vector, and
% $x_1,x_2,\cdots,x_n$ decision variables. The function
% $f$ is called the objective function. The set
% \begin{equation}\tag*{(456)} % 这里同理，其它不再一一指定。
% S=\left\{x\in\Re^n\bigm|g_j(x)\le 0,\,j=1,2,\cdots,p\right\}
% \end{equation}
% is called the feasible set. An element $x$ in $S$ is called a
% feasible solution.
% \end{mpdef}

% \newtheorem{mpdefop}[mpdef]{Definition}
% \begin{mpdefop}
% A feasible solution $x^*$ is called the optimal
% solution of SOP if and only if
% \begin{equation}
% f(x^*)\ge f(x)
% \end{equation}
% for any feasible solution $x$.
% \end{mpdefop}

% One of the outstanding contributions to mathematical programming was known as
% the Kuhn-Tucker conditions\ref{eq:ktc}. In order to introduce them, let us give
% some definitions. An inequality constraint $g_j(x)\le 0$ is said to be active at
% a point $x^*$ if $g_j(x^*)=0$. A point $x^*$ satisfying $g_j(x^*)\le 0$ is said
% to be regular if the gradient vectors $\nabla g_j(x)$ of all active constraints
% are linearly independent.

% Let $x^*$ be a regular point of the constraints of SOP and assume that all the
% functions $f(x)$ and $g_j(x),j=1,2,\cdots,p$ are differentiable. If $x^*$ is a
% local optimal solution, then there exist Lagrange multipliers
% $\lambda_j,j=1,2,\cdots,p$ such that the following Kuhn-Tucker conditions hold,
% \begin{equation}
% \label{eq:ktc}
% \left\{\begin{array}{l}
%     \nabla f(x^*)-\sum\limits_{j=1}^p\lambda_j\nabla g_j(x^*)=0\\[0.3cm]
%     \lambda_jg_j(x^*)=0,\quad j=1,2,\cdots,p\\[0.2cm]
%     \lambda_j\ge 0,\quad j=1,2,\cdots,p.
% \end{array}\right.
% \end{equation}
% If all the functions $f(x)$ and $g_j(x),j=1,2,\cdots,p$ are convex and
% differentiable, and the point $x^*$ satisfies the Kuhn-Tucker conditions
% (\ref{eq:ktc}), then it has been proved that the point $x^*$ is a global optimal
% solution of SOP.

% \subsection{Linear Programming}
% \label{sec:lp}

% If the functions $f(x),g_j(x),j=1,2,\cdots,p$ are all linear, then SOP is called
% a {\em linear programming}.

% The feasible set of linear is always convex. A point $x$ is called an extreme
% point of convex set $S$ if $x\in S$ and $x$ cannot be expressed as a convex
% combination of two points in $S$. It has been shown that the optimal solution to
% linear programming corresponds to an extreme point of its feasible set provided
% that the feasible set $S$ is bounded. This fact is the basis of the {\em simplex
%   algorithm} which was developed by Dantzig as a very efficient method for
% solving linear programming.
% \begin{table}[ht]
% \centering
%   \centering
%   \caption*{Table~1\hskip1em This is an example for manually numbered table, which
%     would not appear in the list of tables}
%   \label{tab:badtabular2}
%   \begin{tabular}[c]{|c|m{0.8in}|c|c|c|c|c|}\hline
%     \multicolumn{2}{|c|}{Network Topology} & \# of nodes &
%     \multicolumn{3}{c|}{\# of clients} & Server \\\hline
%     GT-ITM & Waxman Transit-Stub & 600 &
%     \multirow{2}{2em}{2\%}&
%     \multirow{2}{2em}{10\%}&
%     \multirow{2}{2em}{50\%}&
%     \multirow{2}{1.2in}{Max. Connectivity}\\\cline{1-3}
%     \multicolumn{2}{|c|}{Inet-2.1} & 6000 & & & &\\\hline
%     \multirow{2}{1in}{Xue} & Rui  & Ni &\multicolumn{4}{c|}{\multirow{2}*{\tongjithesis}}\\\cline{2-3}
%     & \multicolumn{2}{c|}{ABCDEF} &\multicolumn{4}{c|}{} \\\hline
% \end{tabular}
% \end{table}

% Roughly speaking, the simplex algorithm examines only the extreme points of the
% feasible set, rather than all feasible points. At first, the simplex algorithm
% selects an extreme point as the initial point. The successive extreme point is
% selected so as to improve the objective function value. The procedure is
% repeated until no improvement in objective function value can be made. The last
% extreme point is the optimal solution.

% \subsection{Nonlinear Programming}

% If at least one of the functions $f(x),g_j(x),j=1,2,\cdots,p$ is nonlinear, then
% SOP is called a {\em nonlinear programming}.

% A large number of classical optimization methods have been developed to treat
% special-structural nonlinear programming based on the mathematical theory
% concerned with analyzing the structure of problems.
% \begin{figure}[h]
%   \centering
%   \includegraphics[clip]{tongji-lib-logo.jpg}
%   \caption*{Figure~1\hskip1em This is an example for manually numbered figure,
%     which would not appear in the list of figures}
%   \label{tab:badfigure2}
% \end{figure}

% Now we consider a nonlinear programming which is confronted solely with
% maximizing a real-valued function with domain $\Re^n$.  Whether derivatives are
% available or not, the usual strategy is first to select a point in $\Re^n$ which
% is thought to be the most likely place where the maximum exists. If there is no
% information available on which to base such a selection, a point is chosen at
% random. From this first point an attempt is made to construct a sequence of
% points, each of which yields an improved objective function value over its
% predecessor. The next point to be added to the sequence is chosen by analyzing
% the behavior of the function at the previous points. This construction continues
% until some termination criterion is met. Methods based upon this strategy are
% called {\em ascent methods}, which can be classified as {\em direct methods},
% {\em gradient methods}, and {\em Hessian methods} according to the information
% about the behavior of objective function $f$. Direct methods require only that
% the function can be evaluated at each point. Gradient methods require the
% evaluation of first derivatives of $f$. Hessian methods require the evaluation
% of second derivatives. In fact, there is no superior method for all
% problems. The efficiency of a method is very much dependent upon the objective
% function.

% \subsection{Integer Programming}

% {\em Integer programming} is a special mathematical programming in which all of
% the variables are assumed to be only integer values. When there are not only
% integer variables but also conventional continuous variables, we call it {\em
%   mixed integer programming}. If all the variables are assumed either 0 or 1,
% then the problem is termed a {\em zero-one programming}. Although integer
% programming can be solved by an {\em exhaustive enumeration} theoretically, it
% is impractical to solve realistically sized integer programming problems. The
% most successful algorithm so far found to solve integer programming is called
% the {\em branch-and-bound enumeration} developed by Balas (1965) and Dakin
% (1965). The other technique to integer programming is the {\em cutting plane
%   method} developed by Gomory (1959).

% \hfill\textit{Uncertain Programming\/}\quad(\textsl{BaoDing Liu, 2006.2})

% \section*{References}
% \noindent{\itshape NOTE: these references are only for demonstration, they are
%   not real citations in the original text.}

% \begin{enumerate}[{$[$}1{$]$}]
% \item Donald E. Knuth. The \TeX book. Addison-Wesley, 1984. ISBN: 0-201-13448-9
% \item Paul W. Abrahams, Karl Berry and Kathryn A. Hargreaves. \TeX\ for the
%   Impatient. Addison-Wesley, 1990. ISBN: 0-201-51375-7
% \item David Salomon. The advanced \TeX book.  New York : Springer, 1995. ISBN:0-387-94556-3
% \end{enumerate}

% \chapter{外文资料的调研阅读报告或书面翻译}
% \section{单目标规划}
% 北冥有鱼，其名为鲲。鲲之大，不知其几千里也。化而为鸟，其名为鹏。鹏之背，不知其几
% 千里也。怒而飞，其翼若垂天之云。是鸟也，海运则将徙于南冥。南冥者，天池也。
% \begin{equation}\tag*{(123)}
%  p(y|\mathbf{x}) = \frac{p(\mathbf{x},y)}{p(\mathbf{x})}=
% \frac{p(\mathbf{x}|y)p(y)}{p(\mathbf{x})}
% \end{equation}

% 吾生也有涯，而知也无涯。以有涯随无涯，殆已！已而为知者，殆而已矣！为善无近名，为
% 恶无近刑，缘督以为经，可以保身，可以全生，可以养亲，可以尽年。

% \subsection{线性规划}
% 庖丁为文惠君解牛，手之所触，肩之所倚，足之所履，膝之所倚，砉然响然，奏刀騞然，莫
% 不中音，合于桑林之舞，乃中经首之会。
% \begin{table}[ht]
% \centering
%   \centering
%   \caption*{表~1\hskip1em 这是手动编号但不出现在索引中的一个表格例子}
%   \label{tab:badtabular3}
%   \begin{tabular}[c]{|c|m{0.8in}|c|c|c|c|c|}\hline
%     \multicolumn{2}{|c|}{Network Topology} & \# of nodes &
%     \multicolumn{3}{c|}{\# of clients} & Server \\\hline
%     GT-ITM & Waxman Transit-Stub & 600 &
%     \multirow{2}{2em}{2\%}&
%     \multirow{2}{2em}{10\%}&
%     \multirow{2}{2em}{50\%}&
%     \multirow{2}{1.2in}{Max. Connectivity}\\\cline{1-3}
%     \multicolumn{2}{|c|}{Inet-2.1} & 6000 & & & &\\\hline
%     \multirow{2}{1in}{Xue} & Rui  & Ni &\multicolumn{4}{c|}{\multirow{2}*{\tongjithesis}}\\\cline{2-3}
%     & \multicolumn{2}{c|}{ABCDEF} &\multicolumn{4}{c|}{} \\\hline
% \end{tabular}
% \end{table}

% 文惠君曰：“嘻，善哉！技盖至此乎？”庖丁释刀对曰：“臣之所好者道也，进乎技矣。始臣之
% 解牛之时，所见无非全牛者；三年之后，未尝见全牛也；方今之时，臣以神遇而不以目视，
% 官知止而神欲行。依乎天理，批大郤，导大窾，因其固然。技经肯綮之未尝，而况大坬乎！
% 良庖岁更刀，割也；族庖月更刀，折也；今臣之刀十九年矣，所解数千牛矣，而刀刃若新发
% 于硎。彼节者有间而刀刃者无厚，以无厚入有间，恢恢乎其于游刃必有余地矣。是以十九年
% 而刀刃若新发于硎。虽然，每至于族，吾见其难为，怵然为戒，视为止，行为迟，动刀甚微，
% 謋然已解，如土委地。提刀而立，为之而四顾，为之踌躇满志，善刀而藏之。”

% 文惠君曰：“善哉！吾闻庖丁之言，得养生焉。”


% \subsection{非线性规划}
% 孔子与柳下季为友，柳下季之弟名曰盗跖。盗跖从卒九千人，横行天下，侵暴诸侯。穴室枢
% 户，驱人牛马，取人妇女。贪得忘亲，不顾父母兄弟，不祭先祖。所过之邑，大国守城，小
% 国入保，万民苦之。孔子谓柳下季曰：“夫为人父者，必能诏其子；为人兄者，必能教其弟。
% 若父不能诏其子，兄不能教其弟，则无贵父子兄弟之亲矣。今先生，世之才士也，弟为盗
% 跖，为天下害，而弗能教也，丘窃为先生羞之。丘请为先生往说之。”
% \begin{figure}[h]
%   \centering
%   \includegraphics{hello}
%   \caption*{图~1\hskip1em 这是手动编号但不出现索引中的图片的例子}
%   \label{tab:badfigure3}
% \end{figure}

% 柳下季曰：“先生言为人父者必能诏其子，为人兄者必能教其弟，若子不听父之诏，弟不受
% 兄之教，虽今先生之辩，将奈之何哉？且跖之为人也，心如涌泉，意如飘风，强足以距敌，
% 辩足以饰非。顺其心则喜，逆其心则怒，易辱人以言。先生必无往。”

% 孔子不听，颜回为驭，子贡为右，往见盗跖。

% \subsection{整数规划}
% 盗跖乃方休卒徒大山之阳，脍人肝而餔之。孔子下车而前，见谒者曰：“鲁人孔丘，闻将军
% 高义，敬再拜谒者。”谒者入通。盗跖闻之大怒，目如明星，发上指冠，曰：“此夫鲁国之
% 巧伪人孔丘非邪？为我告之：尔作言造语，妄称文、武，冠枝木之冠，带死牛之胁，多辞缪
% 说，不耕而食，不织而衣，摇唇鼓舌，擅生是非，以迷天下之主，使天下学士不反其本，妄
% 作孝弟，而侥幸于封侯富贵者也。子之罪大极重，疾走归！不然，我将以子肝益昼餔之膳。”


% \chapter{其它附录}
% 其它附录的内容可以放到这里，当然如果你愿意，可以把这部分也放到独立的文件中，然后
% 将其\verb|\input| 到主文件中。